Atkin-Lehner |
2- 3+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
3192k |
Isogeny class |
Conductor |
3192 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
256 |
Modular degree for the optimal curve |
Δ |
19152 = 24 · 32 · 7 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ 0 -2 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-43,124] |
[a1,a2,a3,a4,a6] |
Generators |
[1:9:1] |
Generators of the group modulo torsion |
j |
562432000/1197 |
j-invariant |
L |
2.8369448947586 |
L(r)(E,1)/r! |
Ω |
3.8678268950017 |
Real period |
R |
0.733472560115 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6384j1 25536w1 9576i1 79800l1 |
Quadratic twists by: -4 8 -3 5 |